The purpose of this project is to develop methodology for analyzing molecular population genetics data. Work has focused on the use of nonparametric methods for localizing susceptibility loci for complex diseases and quantitative traits in humans. Family-based tests of association are now often used when trying to fine-map a disease susceptibility locus. Recently several tests of linkage and association have been proposed that use nuclear families with multiple affected and unaffected sibs rather than just case-parent triads. We propose a test that generalizes these previous tests. Formula were derived to calculate the power of the test for a randomly mating population. and these power calculations were used to determine conditions when it is advantageous to include unaffected sibs in the analysis. Work has continued on the pedigree equilibrium test (PDT). It was discovered that for certain pedigree structures there was a bias in the test. Two modifications of the test were proposed that correct the bias. The PDT was proposed to take advantage of data in large pedigrees that were collected for other purposes. Clearly when designing a study for association analysis it is important to know whether resources should be directed toward collecting a large number of nuclear families or fewer large families. Using computer simulation we compared the power of the PDT in families of different size and structure, holding the total number of individuals genotyped constant. Our results suggest that for many complex diseases the power may be similar for families of different sizes with a fixed number of individuals in the sample, but specific design recommendations will depend on the genetic model and the family structure.